1. Technical Field
The present invention relates to a flexural vibration piece that vibrates in a flexural mode and an oscillator using the same.
2. Related Art
As a flexural vibration piece that vibrates in a flexural mode in the related art, a tuning fork-type flexural vibration piece has been widely used in which a pair of vibration arms are extended in parallel to each other from a base formed of a base material such as a piezoelectric material and are caused to horizontally vibrate toward each other and away from each other. When the vibration arms of the tuning fork-type flexural vibration piece are excited, the occurrence of the vibration energy loss causes a reduction in performance of the vibration piece, such as an increase in CI (Crystal Impedance) value or a reduction in Q value. For preventing or decreasing such a vibration energy loss, various measures have been taken in the related art.
For example, a tuning fork-type quartz vibration piece has been known in which a notch or a notch groove having a predetermined depth is formed on both side portions of a base from which vibration arms extend (for example, refer to JP-A-2002-261575 and JP-A-2004-260718). In the tuning fork-type quartz vibration piece, when the vibration of the vibration arms includes also a vertical component, the notch or the notch groove reduces the leakage of vibration from the base. Therefore, the confinement effect of vibration energy is enhanced to control the CI value and prevent irregularities in CI values between vibration pieces.
In addition to the mechanical vibration energy loss, vibration energy loss is also caused by heat conduction due to the temperature difference caused between a compression portion on which a compressive stress of the vibration arms that perform flexural vibration acts and an extension portion on which a tensile stress acts. A reduction in Q value caused by the heat conduction is called a thermoelastic loss effect.
For preventing or suppressing the reduction in Q value due to the thermoelastic loss effect, a tuning fork-type vibration piece in which a groove or a hole is formed on the center line of vibration arms (vibration beams) having a rectangular cross section is disclosed in, for example, JP-UM-A-2-32229.
JP-UM-A-2-32229 describes, based on a well-known relational formula between strain and stress in the case of internal friction in solids generally caused by temperature difference, that in the thermoelastic loss in a vibration piece in a flexural vibration mode, the Q value becomes minimum in the case where the number of relaxation oscillations fm=1/(2πτ) (where τ is a relaxation time) when the number of vibrations changes. The relationship between the Q value and frequency generally expressed as the curve F in FIG. 11 (for example, refer to C. Zener and other two persons, “Internal Friction in Solids III. Experimental Demonstration of Thermoelastic Internal Friction”, PHYSICAL REVIEW, Jan. 1, 1938, Volume 53, p. 100-101). In the drawing, the frequency at which the Q value takes a minimum value Q0 is a thermal relaxation frequency f0 (=1/(2πτ)), that is, the thermal relaxation frequency f0 is the same as the number of relaxation oscillations fm.
Description will be made specifically with reference to the drawing. In FIG. 10, a tuning fork-type quartz vibration piece 1 of JP-UM-A-2-32229 includes two vibration arms 3 and 4 extending from a base 2 in parallel to each other. The vibration arms 3 and 4 are provided with linear grooves or holes 6 and 7 on the respective center lines. When a predetermined drive voltage is applied to a not-shown excitation electrode of the tuning fork-type quartz vibration piece 1, the vibration arms 3 and 4 perform flexural vibration toward each other and away from each other as indicated by imaginary lines (two-dot chain lines) and arrows in the drawing.
Due to the flexural vibration, a mechanical strain occurs in regions of root portions of the respective vibration arms 3 and 4 at the base 2. That is, in the root portion of the vibration arm 3 at the base 2, a first region 10 on which a compressive stress or a tensile stress acts due to the flexural vibration and a second region 11 having a relationship in which a tensile stress acts thereon when a compressive stress acts on the first region 10 and a compressive stress acts thereon when a tensile stress acts on the first region 10 are present. In the first region 10 and the second region 11, temperature increases when a compressive stress acts, while temperature decreases when a tensile stress acts.
Similarly, in the root portion of the vibration arm 4 at the base 2, a first region 12 on which a compressive stress or a tensile stress acts due to the flexural vibration and a second region 13 having a relationship in which a tensile stress acts thereon when a compressive stress acts on the first region 12 and a compressive stress acts thereon when a tensile stress acts on the first region 12 are present. In the first region 12 and the second region 13, temperature increases when a compressive stress acts, while temperature decreases when a tensile stress acts.
Due to the thus generated temperature gradient, inside the root portions of the respective vibration arms 3 and 4 at the base 2, heat conduction occurs between the first region 10 and the second region 11 and between the first region 12 and the second region and 13. The temperature gradient is generated in opposite directions corresponding to the flexural vibration of the vibration arms 3 and 4, and also the heat conduction changes in direction corresponding thereto. Due to the heat conduction, part of the vibration energy of the vibration arms 3 and 4 is constantly lost during vibration as thermoelastic loss. As a result, the Q value of the tuning fork-type quartz vibration piece 1 decreases, which makes it difficult to realize a desired, high performance. In the tuning fork-type quartz vibration piece 1 disclosed in JP-UM-A-2-32229, heat transfer from a compression side to a tensile side is blocked by the grooves or holes 6 and 7 disposed on the respective center lines of the vibration arms 3 and 4, so that the decrease in Q value due to the thermoelastic loss can be prevented or diminished.
However, in the tuning fork-type quartz vibration piece 1 disclosed in JP-UM-A-2-32229, it becomes difficult along with miniaturization to form the grooves or holes having a shape by which a reduction in Q value due to the thermoelastic loss can be prevented or reduced. In addition, there might be a problem that an effect of suppressing the reduction in Q value cannot be sufficiently provided.